Finite Group Databasebeta

C22×#16813622 #28403850

order14464
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC22×#16813622

Splittings

SylowC113 ⋊ C22×C4⋊Q8

Subgroups

subgroupG/H
centerC24C22×D113
commutator, cosocleC22×C113C25
FrattiniC22C24×D113
FittingC22×C42×C113C2
socle, prime radicalC24×C113C23
hypercenterC22×C42D113
hypocenterC113C22×C4⋊Q8
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C24 ◁ C22×C42

1624 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14464

Conjugacy classes & character table

3640 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 17786);